diff --git a/lib/matplotlib/tests/test_scale.py b/lib/matplotlib/tests/test_scale.py
index fc840ba5c429..052923fc7bfe 100644
--- a/lib/matplotlib/tests/test_scale.py
+++ b/lib/matplotlib/tests/test_scale.py
@@ -28,6 +28,16 @@ def test_logit_scales():
     ax.grid(True)
 
 
+@cleanup
+def test_logit_tight_layout():
+    # Check that logit scale works with tight layout
+    fig, axs = plt.subplots(2, 2)
+
+    axs[1, 1].set_yscale('logit')
+    plt.tight_layout()
+    plt.draw()
+
+
 @cleanup
 def test_log_scatter():
     """Issue #1799"""
diff --git a/lib/matplotlib/text.py b/lib/matplotlib/text.py
index 9e2d8be26842..214af64dfc3d 100644
--- a/lib/matplotlib/text.py
+++ b/lib/matplotlib/text.py
@@ -1154,6 +1154,8 @@ def set_position(self, xy):
         """
         self.set_x(xy[0])
         self.set_y(xy[1])
+        if not np.all(np.isfinite(xy)):
+            self.set_visible(False)
 
     def set_x(self, x):
         """